This simplified subproblem \({\hat{\cal P}_{ \rm passive}}\)  is similar to those in [1]}, [2]}, [3]}. Obviously, since the matrix \({\mathbf {\Lambda }}\)  is positive semidefinite, the objective function is convex. Besides, since we have \({{\cal F}} \triangleq \lbrace  {\theta _{r,j}}{\Big |}\left| {{\theta _{r,j}}} \right| \le 1\rbrace \)  according to (REF ), the constraint \(C_2\)  is also convex. Therefore, \({\bf \Theta }^{\rm opt}\)  can be directly obtained by the standard convex tools such as CVX [4]}. Again, we also give a feasible solution to \({\hat{\cal P}_{ \rm passive}}\)  in Appendix .
